Simultaneous Primitive Roots over Finite Rings

N. A. Carella

Simultaneous Primitive Roots over Finite Rings

General Mathematics 2025-01-22 v1

Authors: N. A. Carella

Abstract

This note investigates the average density of prime numbers $p\in[x,2x]$ with respect to a random simultaneous primitive root $g\leq p^{1/2+\varepsilon}$ over the finite rings $\mathbb{Z}/p\mathbb{Z}$ and $\mathbb{Z}/p^2\mathbb{Z}$ as $x \to \infty$ .

Keywords

additive number theory prime numbers prime number theory

Cite

@article{arxiv.2501.10399,
  title  = {Simultaneous Primitive Roots over Finite Rings},
  author = {N. A. Carella},
  journal= {arXiv preprint arXiv:2501.10399},
  year   = {2025}
}

Comments

Twenty Pages. Keywords: Prime number; Primitive root; Simultaneous primitive root; Hensel lemma; Artin Primitive Root Conjecture

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